1. Charged-particle acceleration in PW laser-plasma interaction
Present to International Conference on Frontier of Science
Charged-particle acceleration in PW laser-plasma interaction
X. T. He
Institute of Applied Physics and Computational Mathematics,
Beijing

2. Outline Introduction Electron acceleration by PW laser
3. Proton acceleration by normal and oblique incident PW lasers
4. Plasma density effect on ion beam acceleration
5. Heavy ion acceleration and quark-gluon plasma research
6. Conclusions and discussions

3. 1.Introduction
With development of CPA technology, short-pulse and high-intense laser (PW-1015w) system can provide intensities w/cm2 for each beam. Interaction of the petawatt (PW) laser with matter may accelerate charged particles (electrons, protons and heavy ions) to kinetic energy over GeV. Could PW laser beam accelerating particles serve for high energy physics instead of (or parallel to) accelerators RHIC and LHC in future?
So far only the PW lasers of x100J/0.5ps are used for experiments. New PW lasers are being constructed : 10kJ/4 beams/1-10ps in Japan, 2x2.6kJ/2 beams/1-10ps and NIF in US, 1.5kJ/1 beam/1-5ps (and future SG-IV) in China will be operating in 2-3 years.
In this presentation, charged particle acceleration mechanisms and application to QGP research are presented and discussed

4. 2. Electron acceleration by PW laser-driven wake field
Wake-field: Electrons are accelerated, like surf in laser-driven plasma wave
Some electrons are trapped and accelerated in the bubble as shown in the bubble black rod.
Laser intensity 3x1020w/cm2,electron energy >300MeV is observed (Mangles et al., PRL94(05)

5. 2. Electron resonance acceleration in PW laser-plasma interaction
Resonant acceleration :
Where axial velocity for electron, group velocity for laser.
Maximal kinetic energy ~180MeV for Gaussian CP laser
Maximal kinetic energy ~170MeV for planar laser (Liu and He, PRE2004)

6. 3. Proton acceleration by PW laser incident on normal direction
Electrons driven out of the target front side by PW laser
ponderomotive force set up electrostatic fields that accelerate protons backward against the PW laser direction. On the other hand, the electrons in the target front side can also be accelerated by ponderomotive force, a thin Debye sheath at the garget rear side is generated when electrons penetrate through the target.

7. 3. Proton acceleration by PW laser incident on normal direction
When PW laser beam propagates along the target normal
direction or a small angle, the proton emission cone is also
aligned at same as direction or cone. Furthermore, the
electron sheath has a Gaussian profile, and the central region
as well as the edge of the sheath will expel proton normal to
the surface. The Bragg peak proton energy is at the center the
resulting Gaussian proton beam (Zhang and He, IAEA06).
Electric field E=30GV/cm, laser intensity 1020w/cm2
Energetic proton in the rear CH target

8. 3. Proton acceleration by PW laser incident on normal direction
Protons by PW laser acceleration was verified by experiments
and simulations, see review papers: Plasma phys. Controlled
Fusion 47, B841(05) by M. Roth et al and Fusion Science and
Tech. 49, 412 (06) by M. Borghesi. Experimental results are
shown in the following plot. Laser intensities of up to 1020 w/cm2,
But the pulse duration is < 100fs.

9. 3. Proton acceleration by PW laser incident on normal direction
Protons by PW laser acceleration was verified by experiments
and simulations, see review papers: Plasma phys. Controlled
Fusion 47, B841(05) by M. Roth et al and Fusion Science and
Tech. 49, 412 (06) by M. Borghesi. Experimental results are
shown in the following plot. Laser intensities of up to 1020 w/cm2,
But the pulse duration is < 100fs.

10. 3. Larger oblique angle of PW laser effect on proton acceleration
Numerical simulation conditions (APL,90, (07) by Zhou and He):
(a) Laser intensity I0=3x1020 w/cm2. PF-PIC.
(b) C+ H2+ foil (5eV), thickness: 19< z / micron <26; density: in the propagating direction, there is a linear rise to n0 within 1.0 micron on both sides, n0/100 at z=19.
(c) =0.2, 1, 3 g/cm3
(d)

11. 3. Larger oblique angle of PW laser effect on proton acceleration
Protons and carbon ions accelerated from the front and rear surfaces
of CH target deviate from the normal direction (I=3x1020 w/cm2) due to
non-Gaussian asymmetric sheath field at the target surfaces.

12. 3. Larger oblique angle of PW laser effect on proton acceleration

13. 3. Larger oblique angle of PW laser effect on proton acceleration
, fast electrons are of x-like angle distribution,
; , fast electrons along the target surface generated by surface quasi-static EM fields. Proton density distribution is no longer of a symmetrical Gaussian-like structure. In particular, two-Bragg energy peaks are observed in the backward-accelerated proton beam. It confirms that the front-surface electrons confined by the EM fields can seriously influence on the emission of the backward-accelerated protons. The conversion efficiencies of laser energy into electron energy: 35% (0。) and 18% ( 60。) for >1 MeV. Electron-proton efficiencies : 14% (0。) and 25% (60。) for >2MeV.

14. Plasma density effect on Ion beam acceleration
Relativistic electrons move across the foil,
JAP (07) by Zhou, Yu and He

15. 4. Plasma density effect on Ion beam acceleration

16. 4. Plasma density effect on Ion beam acceleration
I. Lower density
II. Density 1g/cm3
III. Better collimation,
Lower energy

17. 4. Plasma density effect on Ion beam acceleration

18. 5. Heavy ion acceleration and quark-gluon plasma
(1). Finding quark and gluon and understanding QGP in laboratory are an essential mission in high energy physics and high energy astrophysics
(2). Heavy ion beam colliding in the frame of center of mass has achieved QGP information.
In the past 2-3 years, gold nuclei are accelerated by RHIC and collide in the frame of center of mass and the QGP like ideal fluid state was observed.
The QGP state rapidly reaches thermo-equilibrium like equilibrium plasma and can be explained by the fluid equations.

19. Motion equation for QGP：
5. Heavy ion acceleration and quark-gluon plasma
Motion equation for QGP：
Equation for energy density :
For ideal massless QG gas,
Pressure:
The Solution:

20. 5. Heavy ion acceleration and quark-gluon plasma
. Heavy ion beam (high-Z charged particles) could also be accelerated to 100 GeV/ nucleon by PW laser with intensity over 1024 w/cm2 that could be reached by multi-PW beam irradiation.
. PW laser can be used to explore QGP instead of the traditional accelerators, such as RHIC and other new one. Relativistic momentum equation or relativistic Vlasov equation can be used to investigate such heavy ion beam

21. 5. Heavy ion acceleration and quark-gluon plasma
Numerical simulation shows that when laser (intensity I≥1023W/cm2 ) interacts with CH target foil (thickness l~λ), kinetic energy of protons can reach over 4GeV . The laser piston model shows that protons undergo two stages:
longitudinal field acceleration, which is generated by charge separation; laser light reflection to transfer laser energy to target with reflectivity

22. 5. Heavy ion acceleration and quark-gluon plasma
T. Esirkepov et al. PRL 92, (2004).

23. 5. Heavy ion acceleration and quark-gluon plasma
From numerical simulation and analytical estimation,
as t , ion kinetic energy asymptotically
where I is laser intensity, is foil thickness
max ( )
For , ,
The acceleration time tac
and acceleration length Xac=ctac=4.8mm

24. 5. Heavy ion acceleration and quark-gluon plasma
We may estimate kinetic energy of heavy ions from relativistic momentum equation for proton

25. 5. Heavy ion acceleration and quark-gluon plasma
Kinetic energy for heavy ion scaled from proton

26. 5. Heavy ion acceleration and quark-gluon plasma
If proton kinetic energy reaches 100GeV (laser
intensity about 1024w/cm2), and z/A~1/2, then .
It means that in the frame of center of mass, z-particle colliding with kinetic energy 100AGeV may generate QGP.
During the collision of two beams, the number of reaction with cross section is
Where s is the beam sectional area

27. 6. Conclusions and discussions
Charged particle accelerations in PW laser interaction with matters have extensively investigated, to understand mechanism is challenging. Now only the PW lasers of x100J/0.5ps is used for experiments, numerical simulations are limited by computer capability. Today kinetic energy~ GeV is possibly gained.
Due to advancing the study of fast ignition of inertial fusion driven by PW laser, based on present-day CPA technology, to obtain PW laser intensity over 1024w/cm2 is confident if tens beams are used and each beam has 2kJ/1 ps and the focused spot ~ It means that there are possibility to design QGP experiment and to experimentally explore many important phenomena occurring in astrophysics in near future.

28. Thanks